Permutations and Combinations Questions and Answers

Find the product 3 5 4 2 3 5 4 2 Simplify your answer

Evaluate the following expression 7 15 5 7 15 5 Simplify your answer

wer to a subtraction problem is called the sum difference product

What is the additive inverse of 3 The additive inverse of 3 is

Use absolute value to find the following sum 6 9 6 9 Simplify your answer

Find the angle in degrees rounded to one decimal 0 7 19

Find the prime factorization of 322

Write the fraction in lowest terms 115 105 115 105

Write the fractions 1 w and 8 as equivalent fractions with the least common denominator 27

Write the fraction as a decimal Choose the correct answer b OA 0 3 B 0 333 OC 0 3 OD 0 03

Tell the place value of the digit in the given number 593 16 the 1 In the number 593 16 the digit 1 is in the place

Write the fractions 1 9 and 7 as equivalent fractions with the least common denominator 33 7 33 Type integers or fractions

If f x what is the value of f 4 to the nearest thousandth if necessary 17m

1 point You are building a tree house and have bought plans online However the plans are in metric units and your tape measure only has feet The plans say the base of he square tree house should be 3 5 meters How many feet is that round to the nearest hundredth 74 feet 11 48 feet 5 39 feet 21 64 feet

15 GID 2nd choice 3rd choice 4th choice B D C A vs B Votes where A is preferred to B Votes where B is preferred to A A vs C Votes where A is preferred to C Votes where C is preferred to A A vs D Votes where A is preferred to D Votes where D is preferred to A B vs C Votes where B is preferred to C Votes where C is preferred to B Find the winner of the election using the Pairwise Comparison method For each comparison enter the number of times each candidate was preferred to the other Tally the results Points for A Points for B Points for C Points for D A D B C B vs D Votes where B is preferred to D Votes where D is preferred to B Who is the winner OA OB OC C vs D Votes where C is preferred to D Votes where D is preferred to C C A D A B C B A D A B D

If the following represent a model for the height in feet of a tree after x years what is the growth factor f x 8 1 62 0 62 0 38 1 62 0 8 Question 4 25 points After purchasing a home for 160 000 the homeowner noticed the suggested value of her house was depreciating going down each year by 5 for at least the 6 years she lived there Year 1 Year 0 160 000 152 000 130 321 106 147 111 734 Year 2 144 400 If this trend continues how much will the house be worth in 8 years to the nearest dollar 05 700 Year 8

Consider the function m x 2 4 Determine the y intercept for the function m x 0 4 2 0 3 0 0 3 Question 8 10 points Consider the function g x 3x 1 Determine the asymptote for the function g x Oy 0 y 1 Oy 2 y 2 x 3

Sarah Pinski started creating the following pattern in steps aj represents 1 triangle tile a a2 27 40 9 2 represents 3 triangle tiles 1 594 323 4 782 969 a3 If Sarah continues this pattern how many triangle tiles will be needed for the 14th step a

If f x 67 1 what is the value of f 2 to the nearest ten thousandth if necessary

Given t x is a transformation of the graph f x 2 determine which of the below correctly describe t x f x 2x 3 2 1 1 Asymptote y 0 2 3 4 t x 2 x 1 3 Ot x 2 x 1 3 t x 2 x 1 3 t x 2 x 1 3 t x 2 13 Asymptote y 3

Write an equation of the line Price of pair of shoes dollars 50 40 20 10 30 0 50 20 units 0 y Shoe Sales 0 10 units 20 40 60 80 Percent discount X

h x X 1 2 X 1 A x 1 OB x 1 x 1 O C x 1 O D no vertical asymptote

K Solve the system by the addition method x y 4 4x 25y 100 OA 2 0 2 0 OB 0 2 0 2 OC 0 5 0 5 O D 5 0 5 0

K x 30 x OA 0 5 U 6 00 O C 6 5 0 12 8 8 10 8 12 12 CL OB 6 U 5 00 O D 5 6 12 12 8 8

54 2ab 5 ab 20 a b A 6 B 9 C 12 D 13 E 15

Complete the table below The table has been created for you in a Worksheet The worksheet is available as a Google Doc Word or PDF Worksheet If you don t access to Google Docs or Microsoft Word download the PDF and create the worksheet In an application of your choice If you use the Google doc version download your completed worksheet as a PDF You MUST complete the worksheet and upload it as a PDF All gra need to be inserted into the Worksheet and every line Item completed Do NOT upload Individual graphs your work needs to be orga All Images should be original Graphed them using a digital calculator such as Desmos com Resources Desmos User Gulde Export a graph from Desmos by choosing Share and then Export or you can Print them as a PDF Alternatively you can take a screenshot of your graph Insert the graph Images Into the worksheet table Parent Function Notation Parent Function Graph Translation Graph a function that extends only through quadrants 1 2 and 4 If It is not possible to graph through these quadrants chose one or two quadrants and explain the choice Write the function notation for the above function Linear Quadratic Rational Exponential Radical

a Write a function that corresponds to each graph b Write a second function that corresponds to each graph Hint the graphs of sin z and y cos look the same c Explain what it is about the two functions you wrote that makes their graphs the same why do you think this d Explain each answer why did you make the choices you made Grach 11 3 2 T 7 21 5 On 2x 4x 67

Five years ago Cedric and Zoe purchased a home and got a 345 741 mortgage with a 20 year amortization at 3 interest compounded semi annually and biweekly payments The term of the mortgage is now over and they are renewing on the same amortization timeline for another five year term at 4 75 interest compounded semi annually and monthly payments For full marks your answer should be rounded to the nearest cent a What is the balance remaining after the first term Balance 0 00 b How much are the new payments for the second term Payment 0 00

Which of the following relations does the above Hasse diagram represent a Con 3 4 b 2 on 3 4 c Con 3 4 0 d 2 on 3 4 3 4

K Use Gaussian elimination to find the complete solution to the system of equations or state that none exists x y z 7 x y 2z 7 2x 3z 14 OA OB O C O D 3z 3z 32 7 22 2 3z 7 22 2 22 2 7

Find the zeros of the function f x 2x 3 x 1 1 OA none OB 3 OC 3 1 OD 3 1

e dimensions 6 feet by 11 feet 6 feet by 13 feet 8 feet by 11 feet 7 feet by 12 feet

etermine whether the following relation repre 4 6 6 2 9 9 2 2

2 a Find a reduced and full QR factorisation of the matrix 2 1 11 2 0 B b Let A be an m x m matrix and let a be its jth column Using the full QR factorisation of A prove Hadamard s inequality m det A aj 2

Begin by graphing the standard function f x x Then use transformations of this graph to graph the given function h x x 2 O A 5 O B Q G SCLES O C Q O D Ay

A standard train ticket in a certain city costs 2 50 per ride People who use the train also have the option of purchasing a frequent rider pass for 17 25 each month With the pass a ticket costs only 1 75 per ride How m month make the frequent rider pass a better deal than standard train tickets OA 25 or more rides OB 23 or more rides OC 24 or more rides OD 22 or more rides D

we the logarithmic equation Be sure to reject any value that is not in the domain of the original logarithmic expressions 3X 5 A 243 B 15 C 1 465 D 125

K For the given functions f and g find the indicated comp X 2 3 f x g x 3x 2 gof x OA X 4 2 O B X 3 O C X OD 3x 4

are 20 more sophomores than juniors in an 8 AM algebra class If there are 66 students in this class find the number of sophomo 23 sophomores 43 juniors 66 sophomores 46 juniors 86 sophomores 46 juniors 43 sophomores 23 juniors

35 The reciprocal ofis O 2 1000 O 0 10 10 there is none

32 Solve for a 6 09x 8 12 4 06x O x O O 30 O 45 x 1 10 x

mic expressions without using a calculator 1 2 1 2 S X Inx Iny 1 2 lnx IN In y ression as mu P

Darren purchased 250 000 in 364 day T bills 315 days before maturity to yield 2 86 After holding it for 120 days Darren sold the T bill for a yield of 3 25 a How much did Darren pay for the T bills b For how much did Darren sell the T bills c What rate of return per annum did Darren realize on the investment

Calculate the 3x3 determinant 6 0 1 3 277 1 3

Gerry is a restaurant manager and plans to advertise her restaurant The advertising budget is 5000 and she plans to run television and online ads She would like to run at least 5 television ads and 10 online ads A television ad costs 500 and an online ad costs 150 Let x represent the number of television ads and y represent the number of online ads Two of the constraints for this situation are 5 and y 10 What is the other constraint for this situation Enter your answer in the boxes

29 Replace the with the correct symbol or which will make a true statement from the following expression 1 2 V 11 30 Is AGHI a right triangle if the length of the three sides are 13 11 and 21 O cannot be determined O no O yes 31 Solve the systems of linear equations using a graphing method y 3x 17 y 4x 11 O 5 4 O 4 5 O 5 5 Ono solution parallel lines

8 Use the following scenario and frequency table to answer the question The recreation center is curious to find out if patrons are enjoying the facilities They conduct a random survey and ask patrons if they have a membership or not and if they take any of their classes They then looked at the results Have a membership Do not have a membership Total Attend one or more Attend none of the classes offered classes offered 17 23 14 31 16 39 What kind of relationship does this table describe This table is an example of the principle of independence This table is not an example of the principle of independence O There is not enough information to answer this question Total 40 30 70 9 The slope of a line passing through 7 2 and 10 2 is what If the slope is undefined write undefined

Ernie s deposited 3620 into a savings account that earns 6 5 interested compounded quarterly How much money would be in his account after 4 years Round to the nearest dollar Do not use comma in answer S

Multiply Final answer should be in standard form 2a 1 a 3a 2 What is the third term

e the following triangles 1 In the right angle triangle PQR shown below find the regular Trig Ratios for G P Q 5 12 13 0 R